Non density of stability for holomorphic mappings on P^k

Romain Dujardin (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

A well-known theorem due to Mañé-Sad-Sullivan and Lyubich asserts that J-stable maps are dense in any holomorphic family of rational maps in dimension 1. In this paper we show that the corresponding result fails in higher dimension. More precisely, we construct open subsets in the bifurcation locus in the space of holomorphic mappings of degree d of P^k (C) for every d ≥ 2 and k ≥ 2.

Domaines: Systèmes dynamiques [math.DS]

Romain Dujardin. Non density of stability for holomorphic mappings on P^k. 2016. ⟨hal-01376983v1⟩